Consider the function f(x)=x+sinx defined on R. Answer the following:
a. (i) Find f′(x).
b. (ii) Show that f′(x)≥0 for all x∈R and determine the points where f′(x)=0.
c. (iii) Investigate whether the sign of f′(x) changes at any point where f′(x)=0. Hence, state with reasons whether f has any local maxima or minima on R.
d. (iv) Describe the monotonic nature of f on R.